Agradecimientos:
The work of both authors was supported by the Ministerio de Ciencia y Tecnología under grant BFM 2003-06335-C03-02. The second author was
also partially supported by NATO PST.CLG.979738 and INTAS 03-51-6637.

Resumen:

We study the rate of convergence of interpolating simultaneous rational approximations with partially prescribed poles to so-called Nikishin systems of functions. To this end, a vector equilibrium problem in the presence of a vector external field is solved whWe study the rate of convergence of interpolating simultaneous rational approximations with partially prescribed poles to so-called Nikishin systems of functions. To this end, a vector equilibrium problem in the presence of a vector external field is solved which is used to describe the asymptotic behavior of the corresponding second-type functions which appear.[+][-]